Putting aside your long-term goal for this for the moment, there are indeed many ways you can prepare plywood edges for paint. And as you can imagine there's quite a bit of advice out there on this with various recommendations as a quick Google search will show.
One method that is fairly commonly repeated and seems to work very well from the pics I've seen is also one of the simplest, you just use spackle. Its soft consistency makes it easy to apply and spread, it dries quickly and it is expressly made to be easy to sand. Plus of course it takes paint well.
I'm also concerned about movement with time messing up the edge. ie 10 years later will the plies start to show?
I don't think any of the options you've listed, including edge banding1, can be guaranteed not to have some issues after 10 years of service, particularly in any situation where the plywood needs to be cleaned on any sort of regular basis2.
The one alternative that I think you can be assured it will last the lifetime of the furniture is hardwood edging. There are various ways this can be done depending on the tools you have available, how strong you want the edging to be and whether you need it to add any stiffness3. Here are just a few of the many ways this can be done:
If you glue on hardwood not only will the wood be much thicker and more robust than conventional edge banding it'll be stuck in place with normal woodworking glue and you're in charge of how you clamp it home. So there's no reason it shouldn't last the lifetime of the piece.
There are specialist clamps made for edge clamping but there's no need for any of them. Here are a couple of simple options for clamping edging while the glue dries lifted from a previous Answer:
You can also use tape to provide the clamping force:
Note: it's important with the above method to stretch the tape tight (longer strips than are shown in the right image help with this) and use plenty of strips if you want to provide sufficient pressure to ensure a decent glue bond, although it will likely never match what you can achieve using clamps.
1 Iron-on edge banding is made from real wood and provides a quick, cheap way to hide the edge of plywood and other board materials, but the heat-activated glue is known to fail sometimes.
2 Just wiping down furniture with a damp cloth, using plain water, can be surprisingly damaging over time! This is the chief cause of tabletops warping and contributes greatly to the degradation of the finish, no matter what it is.
3 An important consideration for plywood shelves.